The second 'thing' in your quote is not a sentence, by most generally accepted notions of sentence.
Linguistically, in English (not necessarily so for some other language) a sentence is -defined- (I'm not saying 'should be') as having a noun phrase and a verb phrase. That is an academic definition, which may be more or may be less restrictive than grade school grammarians, and which may be more or may be less restrictive than styles acceptable for publication/email/formal speech/informal speech/etc, etc
Stylistically, a 'sentence' that is missing a verb is not considered good style in written publications, and would show a lack of writing experience which would get you thrown out of a job for a newspaper, or would stand out as 'poor grammar' in an essay for a university application.
Of course, people (even English speakers) go around making utterances that don't include verbs, or verbs without nouns, or quite often just plain interjections. And they're not berated for that.
So whether you call your things sentences or not, in a serious narrative (fiction or non-fiction) especially for an educational institution, missing a verb is considered 'bad grammar'. For other things (more loose narratives, poetry, fill in the blank answers on tests, etc) a verb might be optional depending on what you want to get across.